54/x=x-3

Solution for 54/x=x-3 equation:

54/x=x-3

We move all terms to the left:

54/x-(x-3)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

54/x-x+3=0

We multiply all the terms by the denominator


-x*x+3*x+54=0

We add all the numbers together, and all the variables

3x-x*x+54=0

Wy multiply elements

-1x^2+3x+54=0

a = -1; b = 3; c = +54;
Δ = b2-4ac
Δ = 32-4·(-1)·54
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*-1}=\frac{12}{-2}
=-6
$